Simplify the following expression and state the condition under which the simplification is valid: $y = \dfrac{n^2 + 5n}{n^2 + 11n + 30}$
Explanation: First factor the expressions in the numerator and denominator. $ \dfrac{n^2 + 5n}{n^2 + 11n + 30} = \dfrac{(n)(n + 5)}{(n + 6)(n + 5)} $ Notice that the term $(n + 5)$ appears in both the numerator and denominator. Dividing both the numerator and denominator by $(n + 5)$ gives: $y = \dfrac{n}{n + 6}$ Since we divided by $(n + 5)$, $n \neq -5$. $y = \dfrac{n}{n + 6}; \space n \neq -5$